Question
Elizabeth owns a jewerly-making company. She estimate that she has about 4.3x10 to the power of 11 beads in her inventory. The average mass of one bead is 1.1x10 to the power of 4 mg. What is the mass of all the beads in her inventory
Answers
GPT-4o mini
To find the total mass of all the beads in Elizabeth's inventory, we can multiply the estimated number of beads by the average mass of one bead.
The estimated number of beads is \( 4.3 \times 10^{11} \) and the average mass of one bead is \( 1.1 \times 10^{4} \) mg.
Calculating the total mass:
\[
\text{Total Mass} = \text{Number of Beads} \times \text{Mass of One Bead}
\]
\[
\text{Total Mass} = (4.3 \times 10^{11}) \times (1.1 \times 10^{4})
\]
Now, we can multiply the coefficients and add the exponents:
1. Multiply the coefficients: \( 4.3 \times 1.1 = 4.73 \).
2. Add the exponents: \( 11 + 4 = 15 \).
So,
\[
\text{Total Mass} = 4.73 \times 10^{15} \text{ mg}
\]
Therefore, the mass of all the beads in Elizabeth's inventory is \( 4.73 \times 10^{15} \) mg.
The estimated number of beads is \( 4.3 \times 10^{11} \) and the average mass of one bead is \( 1.1 \times 10^{4} \) mg.
Calculating the total mass:
\[
\text{Total Mass} = \text{Number of Beads} \times \text{Mass of One Bead}
\]
\[
\text{Total Mass} = (4.3 \times 10^{11}) \times (1.1 \times 10^{4})
\]
Now, we can multiply the coefficients and add the exponents:
1. Multiply the coefficients: \( 4.3 \times 1.1 = 4.73 \).
2. Add the exponents: \( 11 + 4 = 15 \).
So,
\[
\text{Total Mass} = 4.73 \times 10^{15} \text{ mg}
\]
Therefore, the mass of all the beads in Elizabeth's inventory is \( 4.73 \times 10^{15} \) mg.